Odd dimensional nonlocal Liouville conformal field theories

We construct Euclidean Liouville conformal field theories in odd number of dimensions. The are nonlocal and non-unitary with a log-correlated field, ${\cal Q}$-curvature background, an exponential Liouville-type potential. study the classical quantum properties these including finite entanglement entropy part sphere partition function $F$, boundary anomaly vertex operators' correlation functions. derive analogue even-dimensional DOZZ formula its semi-classical approximation.